The sample average is a random variable and A)is a single number and as a result cannot have a distribution. B)has a probability distribution called its sampling distribution. C)has a probability distribution called the standard normal distribution. D)has a probability distribution that is the same as for the Y₁,..., Y_n i.i.d. variables.

Question

Quizplus · Accepted Answer

The sample average has a probability distribution called its sampling distribution, which describes the distribution of all possible sample means of a given sample size taken from a population. This distribution allows us to make inferences about the population mean based on sample data. The other choices are incorrect because the sample average is not a single number (it varies from sample to sample) and does not have the standard normal distribution or the same distribution as other independent and identically distributed variables.

The Sample Average Is a Random Variable and